Commutative laws
If A, B are two sets, then..
If A, B are two sets, then..Introduction
A set of numbers arranged in a definite order according to some definite rule is called a sequence . Sequences have wide applications. For example, the amount of money in a fixed deposit in a bank, over a number of years increases in a sequenc..
Introduction
The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Inducti..
The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Inducti..Real Numbers
The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real number..
The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real number..Sequences and Series
Sequence - A set of numbers arranged in a definite order according to some definite rule is called a sequence. or A sequence is a function whose domain is the set N of natural numbers. It is customary to denote a sequence by a letter 'a' and the image a(n) or t(n), n N under 'a'..
Example:
E = {x : x 2 = 9 and 3x = 6} is an empty set because there is no number that can satisfy both x 2 = 9 and 3x = 6..
E = {x : x 2 = 9 and 3x = 6} is an empty set because there is no number that can satisfy both x 2 = 9 and 3x = 6..Subsets
If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A B. ..
If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A B. ..Question 1
Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Kerala..
Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Kerala..Introduction
Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number system consists of the ..
Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number system consists of the ..Complex Numbers Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number system consists of the ..
Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number system consists of the ..See what our Users say :
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